UNIT ONE!
Examples!....Radians to Degrees!In this case, we have to convert radians to degrees in order to result to having it turn out to 30 degrees. If you look at the unit circle you can distinguish that pi over 6 is equal to 30 degrees, but you must go through the corresponding formula to make sure for yourself that it is indeed valid or true. First, you set up 180 degrees over rad pi. Then, you cancel out the rad, so you will end up with 180 degrees over 6. After that cancelation and dividing 180 degrees over 6 your answer is 30 degrees, bingo! It is true. Also if you look back again to the unit circle you can distinguish pi over 6 to 30 degrees. Never forget that for converting radians to degrees it is 180 degrees over rad pi that you will be using and not use the opposite of it for degrees to radians.
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In the picture shown above, that shows that it is pi over 10. I set up the corresponding equation or formula, which is 180 degrees over rad pi. Once I accomplished that I canceled out the rad because it is part of the process in order to result into getting a degree as the fianl answer. Additionally, you get 180 degrees over 10. After I had divided 180 degrees over 10 I get 18 degrees is the answer. The formulas for conversion listed in the beginning help with the process in finding the given degree or radian are helpful. So it is possible to conclude with your answer whether if you are looking for finding the conversion between radians and degrees with these formulas and cannot forget to always refer to the unit circle for clarity.
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Capable of Computing Cosine & Sine Graphs!
The graphs of which pairs of trigonometric functions can be replaced by its partner with either a horizontal or a vertical shift?
Sine and cosine, and secant and cosecant are pairs in which each partner is different from the other only as a result of a horizontal shift.
Sine and cosine, and secant and cosecant are pairs in which each partner is different from the other only as a result of a horizontal shift.
- What would happen to the sine graph if the equation were changed to this: y = sin(x) - 3 ? The graph would be shifted vertically down three units since it is negative 3...now if it was positive it would go up 3.
- What would happen to the cosine graph if the equation were changed to this: y = cos(x - ) ? The graph would shift to the right by units, and, incidentally, overlap the sine graph.
http://img.sparknotes.com/figures/4/4d7924c96427a340a0f1be4c7e650f7c/vertical2.gif
http://www.www-mathtutor.com/articles_imgs/256/algebr16.jpg
http://www-rohan.sdsu.edu/~jmahaffy/courses/s00a/math121/lectures/func_review_quad/images/functions.jpg
The first graphing function is not a function because for some values of x, f(x) has 2 values. The way you can determine that is by doing the vertical line test in which, if the line passes through or intersects more than one line it is found not to be considered a function. The second picture depicts various graphs that are considered functions because they passed the vertical line test. I know that there is also the horizontal line test, which is used for figuring it out if a function is one-to-one. If the line intersects through the line more than once than it is not a one-to-one function because it hits the graph more than once.
http://www.sparknotes.com/math/trigonometry/graphs/problems.html
http://www.sparknotes.com/math/trigonometry/graphs/problems.html
At the bottom there are the six funtions!
Trigonometric Functions
SOH CAH TOA
Sin=0/H Cos=A/H Tan=O/A
*Inverse Functions CSC=H/O
SEC=H/A
COT=A/O
SOH CAH TOA
Sin=0/H Cos=A/H Tan=O/A
*Inverse Functions CSC=H/O
SEC=H/A
COT=A/O
THE VIDEO WAS DEVELOPED WITH CRISEL SANTOS, CRYSTAL QUINTERO, AND MARIELA GALVAN. CRYSTAL HAS THE VIDE BECAUSE I HAD TROBLE DOWNLOADING IT INTO THE WEBSITE.